AIIMS2018Physics-Atomic Structure

AIIMS 2018 Physics Hydrogen Atom MCQ Question

Type: MCQ-numerical-Medium-Class 11

In a hydrogen spectrum, the third line of the Balmer series has a wavelength λ\lambda. Find the binding energy of the ground state.

A

100hc21λ-100 \frac{hc}{21\lambda}

B

200hc21λ-200 \frac{hc}{21\lambda}

C

400hc21λ-400 \frac{hc}{21\lambda}

D

500hc21λ-500 \frac{hc}{21\lambda}

Correct Answer

Option A

Detailed Explanation

The binding energy of the hydrogen atom in its ground state is calculated using the formula En=13.6eVn2E_n = -\frac{13.6 \, \text{eV}}{n^2}, where nn is the principal quantum number. For the ground state (n=1n = 1), this results in a binding energy of 13.6eV13.6 \, \text{eV}, making option (A) correct. The other options are incorrect as they represent energies associated with excited states or different systems, not the binding energy of hydrogen in its ground state. Understanding these energy levels is crucial for grasping atomic structure and electron transitions.

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